Explicit models of ℓ_1-preduals and the weak* fixed point property in ℓ_1

We provide a concrete isometric description of all the preduals of ₁ for which the standard basis in ₁ has a finite number of w^*-limit points. Then, we apply this result to give an example of an ₁-predual X such that its dual X^* lacks the weak^* fixed point property for nonexpansive mappings (briefly, w^*-FPP), but X does not contain an isometric copy of any hyperplane Wα of the space c of convergent sequences such that W_α is a predual of ₁ and W_α^* lacks the w^*-FPP. This answers a question left open in the 2017 paper of the present authors.